Betweenness centrality

In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. Betweenness centrality measures how frequently a node appears on the shortest path between other nodes in the graph. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices, that is, there exists at least one path such that either the number of edges that the path passes through (for unweighted graphs) or the sum of the weights of the edges (for weighted graphs) is minimized.

Betweenness centrality was devised as a general measure of centrality:. It applies to a wide range of problems in network theory, including problems related to social networks, biology, transport, and scientific cooperation. Although earlier authors had intuitively described centrality in terms of betweenness, Freeman (1977) gave the first formal definition of betweenness centrality.

Betweenness centrality has wide application in network theory; it measures the extent to which nodes lie between one another. For example, in a telecommunications network, a node with higher betweenness centrality would have more control over the network because more information flows through it.